Simplify the following expression and state the condition under which the simplification is valid. $p = \dfrac{9a^3 - 36a^2 + 36a}{7a^2 + 35a - 98}$
Explanation: First factor out the greatest common factors in the numerator and in the denominator. $ p = \dfrac {9a(a^2 - 4a + 4)} {7(a^2 + 5a - 14)} $ $ p = \dfrac{9a}{7} \cdot \dfrac{a^2 - 4a + 4}{a^2 + 5a - 14} $ Next factor the numerator and denominator. $ p = \dfrac{9a}{7} \cdot \dfrac{(a - 2)(a - 2)}{(a - 2)(a + 7)}$ Assuming $a \neq 2$ , we can cancel the $a - 2$ $ p = \dfrac{9a}{7} \cdot \dfrac{a - 2}{a + 7}$ Therefore: $ p = \dfrac{ 9a(a - 2)}{ 7(a + 7)}$, $a \neq 2$